Some web pages cannot be opened due to timeout on MS Windows

Question

This is a very strange issue related to one (and only) particular PC in our network running Windows 10.

These two web pages cannot be opened on this PC: https://www.chces-soutezit.cz and https://toulcuvdvur.cz (timeout)

Why is it strange?

1. Both URLs work just fine everywhere else.
2. They do work on the very same UTP cable when connected to other PC.
3. The problem is independent on logged-in user (same ERR_TIMED_OUT)
4. ping, tracert and nslookup all work just fine on them.
5. wget or powershell equivalent doesn't work either.
6. (Yeah, other pages like https://seznam.cz work just fine)
7. Temporarily disabling Firewall: no luck.
8. Booting into Windows Safe Mode: no luck.
9. Just to be sure, we even reinstalled the MS Windows there (!), performed all the updates...: no luck.
10. Here comes the killer: both pages work just fine on the very same machine when GNU/Linux live distro is booted (yeah, wtf?!)

Here is some debugging info:

PS C:\Users\someuser> Invoke-WebRequest -uri seznam.cz -TimeoutSec 30 -OutFile b.html -Verbose -MaximumRedirection 30

VERBOSE: GET seznam.cz/ with 0-byte payload

VERBOSE: received -1-byte response of content type text/html; charset=UTF-8

PS C:\Users\someuser> Invoke-WebRequest -uri toulcuvdvur.cz -TimeoutSec 30 -OutFile a.html -Verbose -MaximumRedirection 30

VERBOSE: GET toulcuvdvur.cz/ with 0-byte payload

Invoke-WebRequest : The operation has timed out.

At line:1 char:1

+ Invoke-WebRequest -uri toulcuvdvur.cz -TimeoutSec 30 -OutFile a.html  ...

+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    + CategoryInfo          : InvalidOperation: (System.Net.HttpWebRequest:HttpWebRequest) [Invoke-WebRequest], WebException

    + FullyQualifiedErrorId : WebCmdletWebResponseException,Microsoft.PowerShell.Commands.InvokeWebRequestCommand


PS C:\Users\someuser> ping -n1 toulcuvdvur.cz

Bad value for option -n1, valid range is from 1 to 4294967295.

PS C:\Users\someuser> ping -n 1 toulcuvdvur.cz


Pinging toulcuvdvur.cz [89.221.213.53] with 32 bytes of data:

Reply from 89.221.213.53: bytes=32 time=12ms TTL=55


Ping statistics for 89.221.213.53:

    Packets: Sent = 1, Received = 1, Lost = 0 (0% loss),

Approximate round trip times in milli-seconds:

    Minimum = 12ms, Maximum = 12ms, Average = 12ms

PS C:\Users\someuser> Invoke-WebRequest -uri toulcuvdvur.cz -TimeoutSec 30 -OutFile a.html -Verbose -MaximumRedirection 30

VERBOSE: GET toulcuvdvur.cz/ with 0-byte payload

Invoke-WebRequest : The operation has timed out.

At line:1 char:1

+ Invoke-WebRequest -uri toulcuvdvur.cz -TimeoutSec 30 -OutFile a.html  ...

+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    + CategoryInfo          : InvalidOperation: (System.Net.HttpWebRequest:HttpWebRequest) [Invoke-WebRequest], WebException

    + FullyQualifiedErrorId : WebCmdletWebResponseException,Microsoft.PowerShell.Commands.InvokeWebRequestCommand


PS C:\Users\someuser> nslookup

Default Server:  UnKnown

Address:  10.204.52.103


> toulcuvdvur.cz

Server:  UnKnown

Address:  10.204.52.103


Non-authoritative answer:

Name:    toulcuvdvur.cz

Address:  89.221.213.53


>

PS C:\Users\someuser>

What the hack (?) Any clues?